Camera calibrating apparatus and method

ABSTRACT

A camera calibrating apparatus uses a calibration target in combination with a laser source generating a laser beam defining a calibration plane and intersecting the camera field of view to define an object imaging area. The calibration target includes a frame defining a coplanar arrangement of reference points having known position coordinates within an object reference system. The frame is disposed in a camera calibration position wherein the coplanar arrangement of reference points is substantially parallel to the calibration plane. The target includes an arrangement of light reflecting members protruding from the arrangement of reference points in a direction substantially perpendicular thereto so as to extend within the object imaging area, to allow the camera to capture an image formed by illuminated portions of the light reflecting members. The apparatus further includes image processor means programmed on the basis a calibrated camera model to associate any position coordinates in the object reference system with corresponding position coordinates in an image reference system.

This application claims the benefit of U.S. Provisional Application No.60/573,336 filed May 24, 2004.

FIELD OF THE INVENTION

The present invention relates to the field of object imaging withelectronic cameras, and more particularly to camera calibrating targets,as well as apparatus and methods employing such targets for calibratingelectronic cameras, in combination with laser light source as part ofdetection/measurement instrumentation.

BRIEF DESCRIPTION OF THE BACKGROUND ART

Laser and electronic imaging technologies have been used for many yearsin many product manufacturing applications, particularly for qualitycontrol involving numerous types of measurement such as dimension,shape, profile or surface characteristics such as roughness and presenceof defects. Typically, measurements are based on the well known lasertriangulation ranging principle involving a direct relationship betweenthe distance separating a reference plane and a given point of thesurface of an object under inspection as measured along an axisextending in a direction perpendicular to the surface in one hand, andthe reflected light being shifted from a corresponding referenceposition as observed at the imaging sensor or camera location in theother hand. Thus, following an appropriate calibration step, profiledata as defined by series of calculated distance values forcorresponding points on the surface can be directly derived from lightbeam shifts measurements. A known calibration approach consists ofcurrently establishing the correspondence between each pixel positioncoordinates provided at the imaging sensor within an image referencesystem and the spatial position coordinates of any point located withinan inspection area delimited by the optical field of view of the imagingsensor or camera and the illumination plane defined by the laser beamand with respect to a world or object reference system, using amathematical camera model such as proposed by Roger Tsai in “A versatilecamera calibration technique for High-Accuracy 3D machine visionmetrology using off-the-shelf TV cameras and lenses”, IEEE Journal ofRobotics and Automation, Vol. RA-3, No. 4, August 1987, which model iscalibrated from position coordinates data obtained through initialmeasurements using a calibration target of either of the coplanar ornon-coplanar type. A non-coplanar calibration target consists of astructure defining a three-dimensional arrangement of reference pointshaving known position coordinates within a three-dimensional referencesystem associated with such structure. In use, the structure isaccurately disposed in a camera calibration position with respect to thethree coordinates axis of the reference system and with respect to theillumination plane defined by the laser source beam. The use ofnon-coplanar calibration targets may be required in certain cases wherean unknown optical parameter such as scale factor uncertainty, has to beestimated. However, they require simultaneous and precise alignment withrespect to all three coordinates axis of the reference system, whereascoplanar calibration targets require precise alignment with respect toonly two coordinates axis of the same reference system. Known coplanarand non-coplanar camera calibration targets are disclosed in U.S. Pat.No. 6,621,921 B1, U.S. Pat. No. 6,437,823 B1 and U.S. Pat. No. 6,195,455B1. Although coplanar camera calibration targets are less arduous toalign with the illuminating plane defined by the laser source ascompared with non-coplanar calibration targets, the alignment stillremains a critical operation in order to achieve the measurementaccuracy requirements. Therefore, there is still a need for improvedcoplanar calibration targets as well as apparatus and method using suchimproved targets exhibiting ease of operation while insuring highposition coordinates measurement accuracy.

SUMMARY OF INVENTION

It is therefore a main object of the present invention to provide acamera calibrating target, a camera calibrating apparatus and methodusing such target, which accurate correspondence between actual positioncoordinates within calibration plane defined by a laser beam and theimage position coordinates generated by the camera according to itsspecific optical characteristics while involving minimal targetalignment accuracy requirements.

According to the above main object, from a broad aspect of the presentinvention, there is provided a camera calibrating target for use with alaser source capable of generating a beam of coherent light defining acalibration plane, the camera being characterized by a field of view inthe direction of an optical axis forming a predetermined angle with saidcalibration plane, the beam intersecting the field of view of the camerato define an object imaging area. The camera calibrating targetcomprises a frame defining a coplanar arrangement of reference pointshaving known position coordinates within an object reference systemassociated with the frame and defining at least two dimensions, theframe being capable of being disposed in a camera calibration positionwherein the coplanar arrangement of reference points is substantiallyparallel to the calibration plane. The target further comprises anarrangement of light reflecting members protruding from the arrangementof reference points in a direction substantially perpendicular theretoso as to extend within the object imaging area when the frame isdisposed in the camera calibration position to allow the camera tocapture an image formed by illuminated portions of the light reflectingmembers.

So as to maximize quality of the captured calibration image, thereference points are located with one another within the arrangement andwith respect to the coherent light beam so as to prevent shading ofreflecting members which may adversely affect the illuminated portionsin forming the image.

Conveniently, the two-dimensional arrangement includes a plurality ofreference points series extending substantially transversely to thecoherent light beam and being disposed in parallel spaced apartrelationship in the direction of the light beam from a foremost positionon the frame proximal to the laser source to a rearmost position on theframe distal to the laser source.

Preferably, the respective points of adjacent ones of said series aretransversely shifted with one another within the arrangement and withrespect to the coherent light beam so as to prevent shading ofreflecting members which may adversely affect the illuminated portionsin forming the image.

According to the above main object, from a further broad aspect of theinvention, there is provided a camera calibrating apparatus for use witha laser source capable of generating a beam of coherent light defining acalibration plane, the camera being characterized by intrinsic imagingparameters and a field of view in the direction of an optical axisforming a predetermined angle with the calibration plane, the beamintersecting the field of view of the camera to define an object imagingarea. The apparatus comprises a calibration target including a framedefining a coplanar arrangement of reference points having knownposition coordinates within an object reference system associated withthe frame and defining at least two dimensions, the frame being capableof being disposed in a camera calibration position wherein the coplanararrangement of reference points is substantially parallel to thecalibration plane. The target further includes an arrangement of lightreflecting members protruding from the arrangement of reference pointsin a direction substantially perpendicular thereto so as to extendwithin the object imaging area when the frame is disposed in the cameracalibration position to allow the camera to capture an image formed byilluminated portions of the light reflecting members. The apparatusfurther comprises image processor means for estimating positioncoordinates of the illuminated portions within an image reference systemassociated with the camera, for associating the estimated positioncoordinates of each illuminated portion within the image referencesystem with the known position coordinates of a corresponding one ofsaid reference points in relation with a corresponding one of saidcalibration planes within the object reference system, for calibrating acamera model based on the intrinsic imaging parameters with theassociated known position coordinates and estimated positioncoordinates, and for using the calibrated camera model to associate anyposition coordinates in the object reference system with correspondingposition coordinates in the image reference system.

According to the above main object, from another broad aspect of thepresent invention, there is provided a method of calibrating a cameracharacterized by intrinsic imaging parameters and a field of view in thedirection of an optical axis. The method comprises the steps of: i)generating a beam of coherent light defining a calibration plane; ii)disposing the camera so that its field of view in the direction of itsoptical axis forms a predetermined angle with the calibration plane andso that the beam intersects the field of view of the camera to define anobject imaging area; iii) providing a calibration target including: a) aframe defining a coplanar arrangement of reference points having knownposition coordinates within an object reference system associated withthe frame and defining at least two dimensions; and b) an arrangement oflight reflecting members protruding from the arrangement of referencepoints in a direction substantially perpendicular thereto; iv) disposingthe frame in a camera calibration position wherein the coplanararrangement of reference points is substantially parallel to thecalibration plane so that the light reflecting members extend within theobject imaging area; v) generating with the camera an image formed byilluminated portions of the light reflecting members; vi) estimatingposition coordinates of the illuminated portions within an imagereference system associated with the camera; vii) associating theestimated position coordinates of each illuminated portion within theimage reference system with the known position coordinates of acorresponding one of the reference points within the object referencesystem; viii) calibrating a camera model based on the intrinsic imagingparameters with the associated known position coordinates and estimatedposition coordinates; and ix) using the calibrated camera model toassociate any position coordinates in the object reference system withcorresponding position coordinates in the image reference system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an elevation view of the camera calibration apparatusaccording to a first embodiment of the present invention, showing thecalibration target aligned with the respective light beams generated bytwo laser sources associated with respective electronic camerassubjected to a calibration procedure;

FIG. 2 is a front end view, along lines 2-2 shown in FIG. 1, of thecamera calibration target and laser source of the calibration set up ofthe first embodiment, showing the particular spatial arrangement ofreference points from which protrude the light reflecting members aspart of the calibration target;

FIG. 3 is an enlarged partial view of the camera calibration targetillustrated in FIG. 2, on which the trajectories of light rays are shownto illustrate that the particular arrangement of reference points andassociated reflecting members ensure efficient illumination thereof bylaser beam to prevent shading effect;

FIG. 4 is a process flow diagram showing the main image processing stepsperformed according to a coplanar calibration procedure using thecalibration target of the invention, to associate any positioncoordinates in the object reference system with corresponding positioncoordinates in the image reference system; and

FIG. 5 is a detailed elevation view of the camera calibration target aspart of the embodiment shown in FIG. 1 and shown in two differentpositions, to illustrate that the captured image is not significantlyaffected by a deviation in alignment of the calibration target withrespect to the calibration plane.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Preferred embodiments of camera calibration apparatus and method makinguse of a calibration target according to the invention will now bedescribed in detail. Referring now to FIG. 1, a basic camera calibrationapparatus set up using the calibration target of the invention andgenerally designated at 10, includes a laser source 12, such as aLasiris™ SNF laser supplied by Stocker Yale (Salem, N.H.) for generatinga beam of coherent light represented at 14 being preferably of afan-shaped type as better shown in FIG. 2 so as to define a calibrationplane generally designated at 16 and delimited by axis lines 18, 18′ and28 shown in FIG. 2 as determined by a preset scanning rangecharacterizing laser source 12. As shown in FIG. 1, a camera 20 such asmodel A501K supplied by Basler Vision Technologies (Exton, Pa.), whichis subjected to the calibration procedure, is disposed with respect tothe calibration plane 16 defined by laser source 12 so that its field ofview in the direction of optical axis 22 forms a predetermined angle θwith the calibration plane defined by laser beam 14, which angle θ isformed at an intersection points P_(θ) of the calibration plane asbetter shown in FIG. 2. Angle θ should be preferably of at least 30° forproviding depth to reference points defined by the calibration target,as will be explained later in more detail. It can be seen from FIGS. 1and 2 that the laser beam 14 intersects the field of view of camera 20so as to define and object imaging area generally designated at 24forming a projection within an object reference system generallydesignated at 26 defining at least two dimensions, namely represented byX_(w) axis 28 and Y_(w) axis 30, delimited by X axis 28 betweencoordinates X=X₁ and X=X₂ and by Y axis 30 between coordinates Y=0 andY=Y₁. According to a preferred embodiment, the camera calibrating target32 includes a frame 34, defining a coplanar arrangement of referencepoints 37, 38, 39, 40, 41 as better shown in FIG. 2, which referencepoints have known position coordinates within the object referencesystem 26 associated with frame 34. It can be seen from FIG. 1 in viewof FIG. 2 that the frame 34 is capable of being disposed in a cameracalibration position wherein the coplanar arrangement of referencepoints 37, 38, 39, 40, 41 is substantially parallel to the calibrationplane 16. The calibration target frame 34 may be adjustably maintainedin the camera calibration position using any appropriate support means(not shown). In the example shown in FIGS. 1 and 2, camera and lasersource 12 are angularly oriented with one another so that the objectimaging area 24 corresponding to camera calibration position of targetframe 34 substantially coincides with an object scanning locationintersected by an object travelling path represented by axis 42 asdefined by conveyors 44, 44′ of a transport system adapted to be used incombination with laser source 12 and camera 20 following the calibrationprocedure. It can be seen from FIG. 1 that the calibration target 32further includes an arrangement of light reflecting members 46, 47, 48,49, 50, 51 protruding from the arrangement of reference points 36, 37,38, 39, 40, 41, in a direction substantially perpendicular thereto so asto extend within the object imaging area 24 when the frame 34 isdisposed in the camera calibration position allowing camera 20 tocapture an image formed by illuminated portions of the light reflectingmembers 46, 47, 48, 49, 50, 51. Although the frame 34 is of arectangular shape in the example shown, it is to be understood that anyother appropriate shape may be used, provided that a sufficient numberof adequately distributed reflecting members extend within the objectimaging area.

Turning now to FIG. 3, reference points 36, 37, 38, 39, 40, 41 arelocated with one another within the arrangement and with respect tolight beam 14 so as to prevent shading of reflecting members 47, 48, 49,50, 51 as shown in FIG. 1 which may adversely affect the illuminatedportions thereof in forming the image by camera 20. The externaldiameter of the light reflecting members 46, 47, 48, 49, 50, 51 as wellas their location on frame 34 as defined by corresponding referencepoints 36, 37, 38, 39, 40, 41 are determined considering the cameraresolution, width and height dimensions of the imaging area along X_(w)axis 28 and Y_(w) axis 30, as well as the relative position of the lasersource 12, so as to ensure that all light reflecting members, which areoptimally distributed within the imaging area, receive appropriateillumination. More particularly, the coplanar arrangement is designed toinclude a plurality of reference point series respectively correspondingto points 36, 37, 38, 39, 40, 41 which extend substantially transverselyto coherent light beam 14 as represented by a set of rays in FIG. 3originating from laser source 12, and being disposed in parallel spacedapart relationship in the direction of light beam 14 from a foremostposition on the frame 34 proximal to laser source 12, corresponding toseries of reference points 36, to a rearmost position on frame 34 distalto laser source 12, corresponding to series of reference points 41 inthe example shown. It can be seen from FIG. 3 that the shadow areaextending along any ray axis 52 aligned with any corresponding ray 53 asa result of the illumination of any corresponding reflecting member suchat 46 in the example shown, is offset to any other ray axis associatedwith any other incident light ray that illuminates it. It can also beseen from FIG. 3 that the minimum transverse clearance along X axis 28is set to a value “c” ” that is sufficient to prevent adverse shadingwhile complying with camera image resolution to ensure reliable positioncoordinates determination of each point from the captured image. Inother words, the respective points of adjacent ones of series 36, 37,38, 39, 40 and 41 are transversely shifted with one another within thearrangement and with respect to light beam 14 so as to prevent shadingof deflecting members 47, 48, 49, 50 and 51 which may adversely affectthe illuminated portion thereof in forming the image captured by camera20. It can be appreciated that the spacing between adjacent reflectingmembers 46 of the foremost series must be set at a higher value as theimaging area height is increased. Preferably, an appropriate coating isapplied onto the surface subjected to illumination on eachlight-reflecting member, to provide a resulting reflectance that iscomparable with the reflectance obtained with the real object to beinspected. Since the calibration procedure requires positionidentification of each light-reflecting member on a captured image, eachreflecting member must receive a minimal illumination level from thelaser beam. A minimum identification threshold corresponding to aminimum image grey level, allowing segmentation of the image portioncorresponding to reflecting member as opposed to image background, maybe estimated. With the particular camera used in the present example,such identification threshold has been set to at least 10/255 to preventsegmentation error. The calibration procedure requires establishing acorrespondence between the actual world object coordinates within theobject reference system 26 with image coordinates within the imagereference system derived from the calibration target image. For sodoing, two sorting steps are preferably performed successively on thebasis of estimated image coordinates. Assuming that the actual world,object coordinates are generated line by line, from top to bottom andfrom left to right, knowing the exact number of points on each line, theimage coordinates are first sorted from top to bottom and then from leftto right within each line. Hence, exact correspondence between imagecoordinates and object coordinates can be obtained, provided thecalibration target is adequately positioned. The calibration target 32must be positioned in such a manner that none of the reference pointswithin any series, for instance series 36, located along Y_(w) axis 30over any point of a following reference points series, such as series 37for the instant example. It is to be understood that any otherappropriate manner to establish a correspondence between the objectcoordinates and the image coordinates, such as using a predeterminedmatching data file stored in the computer, can be employed.

Conveniently, in cases where more than one surface or side of an objecthas to be scanned simultaneously, a same camera calibration target 32can be provided with complementary sets of reference points seriesdesignated at 36′, 37′, 38′, 39′, 40′, 41′ in FIG. 2 and correspondinglight reflecting members 46′, 47′, 48′, 49′, 50′, 51′ as shown in FIG. 1which are disposed symmetrically with respect to X axis 28 in theexample shown, as part of a complementary section 54 provided on thecalibration target 32 It is to be understood that a different,non-symmetrical configuration may also be used depending on the specificapplication contemplated. For example, camera 20′ may be chosen to havedifferent imaging resolution as compared to camera 20, and the spatialdistribution and diameter of the reflecting members provided on targetcomplementary section 32 may be set accordingly. Furthermore, in a casewhere articles to be inspected while carried by conveyers 44, 44′ shownin FIG. 1 exhibit thickness variations so that the position of theirrespective top surfaces varies with reference to axis Y_(w) 30, thefield of view characterizing camera 20 must be different to the field ofview of camera 20′ which scans article bottom surfaces whose positionwith reference to axis Y_(w) 30 is substantially maintained at the levelof conveyers 44,44′. The complementary section 54 of calibration target32 can be used with a further laser source 12′ for generating a secondlaser beam 14′, associated with a further camera 20′ characterized witha complementary field of view in the direction of its optical axis 22′forming a predetermined angle θ′ with a complementary calibration plane16′ delimited bv axis lines 19, 19′ and associated with further camera12′. The calibration plane 16′ is aligned with calibration plane 16 whena single calibration frame for two cameras is used. Although axis lines18, 19 and 18′, 19′ intersect axis X_(w) 28 respectively at same pointsx₃, x₄ since laser sources 12, 12′ use equal fan angles in the exampleshown in FIG. 2, it is to be understood that different fan angles may beset for laser sources 12, 12′, provided that the desired target areasare illuminated. As part of a camera calibrating apparatus using thecalibration target of the present invention, there is provided aprocessor means including an image signal acquisition module 55 forreceiving image signals from either camera 20 or 20′ through lines 59,59′ using commercially available hardware such as model Odyssey X-Pro™supplied by Matrox Electronic System (Dorval, Quebec, Canada) and acomputer 56 having the capability to run the required image analysissoftware that is especially programmed to carry out image processingsteps, as will be explained in detail below with reference to FIGS. 4and 7, using a well-known camera calibrating algorithm based on a cameramodel proposed by Roger Y. Tsai in “A Versatile Camera CalibrationTechnique for High-Accuracy 3D Machine Vision Metrology UsingOff-the-Shelf TV Cameras and Lenses, IEEE Journal of Robotics andAutomation, Vol. RA-3, NO. 4, August 1987, pages 323-344.

A first preferred mode of operation of the camera calibrating target asdescribed above according to a preferred embodiment of the inventionwill now be explained in more detail. The same calibration procedure canbe performed in a same manner for each camera 20, 20′. Referring to FIG.1, the computer 56 sends a control signal to the acquisition module 55through data line 58 for causing thereof to transfer through input dataline 60 the data representing camera image formed by illuminatedportions of light reflecting members 46, 47, 48, 49, 50, 51 or 46′, 47′,48′, 49′, 50′, 51′ as received from either camera 20 or 20′ depending onthe computer command sent.

Referring now to FIG. 4, the image data represented at 63 in the processflow diagram can be obtained as follows. In order to prevent imagecontamination due to background pixels in the identification of imagepoints corresponding to reference points provided on the calibrationtarget, a preliminary image processing algorithm is preferably performedon the raw image captured by the camera 20. Such algorithm typicallyrequires that all reference points of the calibration target are madevisible in the image, and when background contamination areas exist inthe image, such areas are individually smaller than the illuminatedportion of each reflecting member, or their respective grey levels arelower than a preset detection threshold. According to this algorithm, acurrent threshold is first initialized to the value of the presetminimum threshold. Then the raw image is binarized using the currentthreshold, followed by a detection of all image blobs which respectivearea is higher than the minimum area corresponding to the level ofreflection of the laser beam onto a given reflecting member. If thedetected number of blobs corresponds with the number of reflectionmembers provided on the target, the resulting image containing only thecalculated blobs is generated so as to eliminate any backgroundcontamination. Otherwise, the current threshold is incremented and thealgorithm is repeated until the above condition is satisfied. Then, themass centre of each image blob is calculated using a well-known imageprocessing subroutine, assuming that the calculated mass centresubstantially corresponds to the actual mass centre position. It is tobe understood that many alternate image pre-processing algorithms may beused to generate reliable image data 63. Hence, image data 63 is used bycomputer 56 at step 70 to estimate position coordinates of theilluminated portions within an image reference system generallydesignated at 57, 57′ in FIGS. 1 and 2 associated with the selectedcamera 20, 20′, respectively formed by X axis 62 in FIG. 1 and Y axis 64in FIG. 2 for camera 20, and X′ axis 66 in FIG. 1 and Y′ axis 68 in FIG.2 for camera 20′ wherein axis Z′ is colinear with optical axis 22′.Since the reference points 36, 37, 38, 39, 40, 41 provided on the upperportion of calibration target 32 shown in FIG. 2 are coplanar, the(X_(w), Y_(w), Z_(w)) object reference system at 26 may be chosen sothat Z_(w)=0, while the origin at 31 is distant from optical Z axis 22at point P_(θ) as well as from Y axis 64 of the image system 57, toensure that T_(Y) component of the translation vector be different fromzero, in order to simplify the computation procedure that will beexplained later in detail. At step 70, the position coordinates (X_(d),Y_(d)) of the illuminated portion within image reference system 57 arecomputed using predetermined intrinsic imaging parameters characterizingthe camera 20. A whole image frame stored in memory of computer 56 isfetched to detect row and column number of each reference point i asexpressed by (X_(fi), Y_(fi)) for i=1, . . . , N, wherein N is the totalnumber of reference points. Then the position coordinates (X_(d), Y_(d))representing the distorted or true image coordinates are derived usingthe following equations: $\begin{matrix}{X_{di} = {s_{x}^{- 1}{d_{x}^{\prime}\left( {X_{fi} - C_{x}} \right)}}} & (1) \\{Y_{di} = {d_{y}\left( {Y_{fi} - C_{y}} \right)}} & (2) \\{d_{x}^{\prime} = {d_{x}\frac{N_{cx}}{N_{fx}}}} & (3)\end{matrix}$wherein (C_(x), C_(y)) are row and column numbers of the centre ofcomputer image frame memory;

d_(x) is the centre-to-centre distance between adjacent sensor elementsin X scanning direction;

d_(y) is centre-to-centre distance between adjacent CCD sensors providedon the camera in the Y direction;

N_(cx) is the number of sensor elements in the X direction;

N_(fx) is the number of pixels in a line as sampled by the computer; and

s_(x) is an image scale factor used to compensate uncertainty aboutestimation of d_(x) and d_(y).When unknown, the scale factor s_(x) can be estimated using a simpletechnique as proposed by R. K. et al. in “R. K. Lenz and R. Y. Tsai,“Techniques for calibration of the scale factor and image centre forhigh accuracy 3D machine vision metrology”, Proc. IEEE Int. Conf.Robotics and Automation, Raleigh, N.C., Mar. 31-Apr. 3, 1987. Then, at afollowing step 72 shown in FIG. 4, the estimated position coordinates(X_(di), Y_(di)) of each illuminated portion within image referencesystem 57 is associated with the known position coordinates (X_(wi),Y_(wi), Z_(wi)) of a corresponding one of the reference points 36, 37,38, 39, 40, 41 within the object reference system 26. At a followingstep 74, a camera model based on intrinsic imaging parameterscharacterizing camera 20 is calibrated with known position coordinates(X_(wi), Y_(wi), Z_(wi)) and estimated position coordinates (X_(di),Y_(di)) that have been associated at prior step 72. For each pair ofposition coordinates (X_(wi), Y_(wi), Z_(wi)), (X_(di), Y_(di)), andusing a number of reference points N being much larger than 5, thefollowing linear equation is used to derive the values of externalparameter related components T_(y) ⁻¹r₁, T_(y) ⁻¹r₂, T_(y) ⁻¹T_(x),T_(y) ³¹ ¹r₄, T_(y) ⁻¹r₅: $\begin{matrix}{{\left\lbrack {{Y_{di}x_{wi}\quad Y_{di}y_{wi}\quad Y_{di}} - {X_{di}x_{wi}} - {X_{di}y_{wi}}} \right\rbrack\begin{bmatrix}{T_{y}^{- 1}r_{1}} \\{T_{y}^{- 1}r_{2}} \\{T_{y}^{- 1}r_{3}} \\{T_{y}^{- 1}r_{4}} \\{T_{y}^{- 1}r_{5}}\end{bmatrix}} = X_{dt}} & (4) \\{\begin{bmatrix}x \\y \\z\end{bmatrix} = {{R\quad\begin{bmatrix}x_{w} \\y_{w} \\z_{w}\end{bmatrix}} + T}} & (5) \\{R \equiv \begin{bmatrix}r_{1} & r_{2} & r_{3} \\r_{4} & r_{5} & r_{6} \\r_{7} & r_{8} & r_{9}\end{bmatrix}} & (6) \\{T \equiv \begin{bmatrix}T_{X} \\T_{X} \\T_{Z}\end{bmatrix}} & (7) \\{X_{u} = {f\frac{x}{z}}} & (8) \\{Y_{u} = {f\frac{y}{z}}} & (9) \\{{X_{d} + D_{x}} = X_{u}} & (10) \\{{Y_{d} + D_{y}} = Y_{u}} & (11) \\{D_{x} = {X_{d}Κ_{1}r^{2}}} & (12) \\{D_{y} = {Y_{d}Κ_{1}r^{2}}} & (13) \\{r = \sqrt{X_{d}^{2} + Y_{d}^{2}}} & (14)\end{matrix}$wherein:

(x,y,z) represent the coordinates of any point within athree-dimensional reference system (not shown) associated with thecamera;

R is the 3×3 rotation matrix as an external parameter;

r₁, . . . r₉ are the rotation coefficient of the rotation matrix R;

T is the translation vector as an external parameter;

T_(x),T_(y),T_(z) are the three components of the translator vector T;

(X_(u),Y_(u)), are ideal, undistorted image coordinates usingperspective projection within the camera three-dimensional referencesystem according to known pinhole camera geometry, which corresponds tothe image reference system 57;

ƒ is the focal length as an intrinsic parameter characterizing thecamera, which is the distance between the image plane defined by axis Xand Y of the image reference system 57 and the optical centrecorresponding to the origin of the camera three-dimensional coordinatessystem;

D_(x),D_(y) represent radial distortion respectively along axis X and Yof image reference system 57, as estimated by the first term of acorresponding infinite series;

(X_(d),Y_(d)) are actual, distorded position coordinates in the imagereference system 57; κ₁ is the radial distortion coefficient;Having solved equation (4) to obtain values of T_(y) ⁻¹r₁, T_(y) ⁻¹r₂,T_(y) ⁻¹T_(x), T_(y) ⁻¹r₄, T_(y) ⁻¹r₅, the values of rotationcoefficient r₁ . . . r₉ as well as the translation componentsT_(x),T_(y) can be computed using the following 2×2 submatrix:$\begin{matrix}{C \equiv \begin{bmatrix}r_{1}^{\prime} & r_{2}^{\prime} \\r_{4}^{\prime} & r_{5}^{\prime}\end{bmatrix} \equiv \begin{bmatrix}{r_{1}/T_{y}} & {r_{2}/T_{y}} \\{r_{4}/T_{y}} & {r_{5}/T_{y}}\end{bmatrix}} & (15)\end{matrix}$if none of whole rows or columns of C vanishes, the component T_(y) canbe computed from: $\begin{matrix}{T_{y}^{2} = \frac{S_{r} - \left\lbrack {S_{r}^{2} - {4\left( {{r_{1}^{\prime}r_{5}^{\prime}} - {r_{4}^{\prime}r_{2}^{\prime}}} \right)^{2}}} \right\rbrack^{1/2}}{2\left( {{r_{1}^{\prime}r_{5}^{\prime}} - {r_{4}^{\prime}r_{2}^{\prime}}} \right)^{2}}} & (16)\end{matrix}$wherein S_(r)=r₁′²+r₂′²+r₄′²+r₅′²;if a given row or column of C vanishes, the component T_(y) can beobtained from:T _(y) ²=(r _(i)′² +r _(j)′²)⁻¹  (17)wherein r_(i)′, r_(j)′ are the elements in the row or column of C thatdo not vanish. Having extracted the square root of component T_(y) fromeither equation (16) or (17), the sign of T_(y) can be determined byfirst choosing an object reference point i associated with computerimage coordinates (X_(fi), Y_(fi)) away from image centre (C_(x), C_(Y))corresponding to object coordinates (X_(wi), Y_(wi), Z_(wi)). Then byassuming that the sign of T_(y) is “+1”, then the following expressionare computed:r ₁=(T _(y) ⁻¹ r ₁)T _(y)  (18)r ₂=(T _(y) ⁻¹ r ₂)T _(y)  (19)r ₄=(T _(y) ⁻¹ r ₄)T _(y)  (20)r ₅=(T _(y) ⁻¹ r ₅)T _(y)  (21)T _(x)=(T _(y) ⁻¹ T _(x))T _(y)  (22)x=r ₁ x _(w) +r ₂ y _(w) +T _(x)  (23)y=r ₄ x _(w) +r ₆ y _(w) +T _(y)  (24)assuming that T_(y) ⁻¹r₁, T_(y) ⁻¹r₂, T_(y) ⁻¹T_(x), T_(y) ⁻¹r₄ andT_(y) ⁻¹r₅ have been previously determined in a manner explained above.Hence, if the values for x and X have a same sign as well as the sign ofy and Y values, then the sign of T_(y) is “+1”, otherwise the sign T_(y)is “−1”. As to the rotation coefficient r₁, . . . r₉ and T_(x), they canbe derived as follows:r ₁=(T _(y) ⁻¹ r ₁)T _(y)  (25)r ₂=(T _(y) ⁻¹ r ₂)T _(y)  (26)r ₄=(T _(y) ⁻¹ r ₄)T _(y)  (27)r ₅=(T _(y) ⁻¹ r ₅)T _(y)  (28)T _(x)=(T _(y) ⁻¹ T _(x))T _(y)  (29)Then, an approximation of focal length ƒ is computed from the followinglinear equations: $\begin{matrix}{{\left\lbrack {y_{i} - {d_{y}Y_{i}}} \right\rbrack\begin{bmatrix}f \\T_{z}\end{bmatrix}} = {w_{i}d_{y}Y_{i}}} & (30) \\{y_{i} = {{r_{4}x_{wi}} + {r_{5}y_{wi}} + {r_{6} \cdot 0} + T_{y}}} & (31) \\{w_{i} = {{r_{7}x_{wi}} + {r_{8}y_{wi}} + {r_{9} \cdot 0}}} & (32)\end{matrix}$if the obtained value for ƒ is positive, the rotation matrix R can becalculated using the following expression: $\begin{matrix}{R = \begin{bmatrix}r_{1} & r_{2} & \left( {1 - r_{1}^{2} - r_{2}^{2}} \right)^{1/2} \\r_{4} & r_{5} & \left( {1 - r_{4}^{2} - r_{5}^{2}} \right)^{1/2} \\r_{7} & r_{8} & r_{9}\end{bmatrix}} & (33)\end{matrix}$wherein s is the inverted sign of the resulting sign of (r₁ r₄+r₂r₅),with r₇, r₈, r₉ being determined from the outer product of the first tworows using the orthonormal and right-handed property of rotation matrixR. If the approximate value of ƒ obtained with equation (30), (31) and(32) is negative, the rotation matrix R can be calculated from thefollowing expression: $\begin{matrix}{R = \begin{bmatrix}r_{1} & r_{2} & {- \left( {1 - r_{1}^{2} - r_{2}^{2}} \right)^{1/2}} \\r_{4} & r_{5} & {- {s\left( {1 - r_{4}^{2} - r_{5}^{2}} \right)}^{1/2}} \\{- r_{7}} & {- r_{8}} & r_{9}\end{bmatrix}} & (34)\end{matrix}$Then, equations (30), (31) and (32) may be used to derive an approximatevalue for translation components T_(z) which will be used along withapproximate values obtained for ƒ and κ₁ an exact solution for theseparameters using the following equations: $\begin{matrix}{{{{d_{y}^{\prime}Y} + {d_{y}Y\quad Κ_{1}r^{2}}} = {f\frac{{r_{4}x_{w}} + {r_{5}y_{w}} + {r_{6}z_{w}} + T_{y}}{{r_{7}x_{w}} + {r_{8}y_{w}} + {r_{9}z_{w}} + T_{z}}}}{{with}\text{:}}} & (35) \\{r = \sqrt{\left( {s_{x}^{- 1}d_{x}^{\prime}X} \right)^{2} + \left( {d_{y}Y} \right)^{2}}} & (36)\end{matrix}$The above equations are solved using a standard optimization scheme suchas well known steepest descent, wherein approximate values for ƒ andT_(z) are used as initial values with κ₁=0. All intrinsic parameters inthe camera model as generally defined in equation (5) having beendetermined, the calibrated camera model so obtained can be used, infinal step 76 shown in FIG. 4 to associate any position coordinates(X_(w), Y_(w), Z_(w)) in the object reference system 26 withcorresponding position coordinates (X_(d), Y_(d)) in the image referencesystem 57.

Turning now to FIG. 5, it can be seen that a misalignment of thecalibration target 32, in rotation within the plane defined by axisY_(w) at 30 and axis Z_(w) at 42 and related to the object referencesystem 26, which rotation is indicated in phantom lines at 78, does nothave any significant effect on the position of the illuminated portions78, 78′ on each reflecting members 46-51 and 46′-51′, even if arelatively important shift “s” may be measured along axis Z_(w) 42 forreflecting members 46 and 46′.

1. A camera calibrating target for use with a laser source capable ofgenerating a beam of coherent light defining a calibration plane, saidcamera being characterized by a field of view in the direction of anoptical axis forming a predetermined angle with said calibration plane,said beam intersecting the field of view of said camera to define anobject imaging area, said target comprising: a frame defining a coplanararrangement of reference points having known position coordinates withinan object reference system associated with said frame and defining atleast two dimensions, said frame being capable of being disposed in acamera calibration position wherein said coplanar arrangement ofreference points is substantially parallel to said calibration plane;and an arrangement of light reflecting members protruding from saidarrangement of reference points in a direction substantiallyperpendicular thereto so as to extend within said object imaging areawhen said frame is disposed in said camera calibration position to allowsaid camera to capture an image formed by illuminated portions of saidlight reflecting members.
 2. The camera calibrating target according toclaim 1, wherein said reference points are located with one anotherwithin said arrangement and with respect to said coherent light beam soas to prevent shading of said reflecting members which may adverselyaffect said illuminated portions in forming said image.
 3. The cameracalibrating target according to claim 1, wherein said coplanararrangement includes a plurality of reference points series extendingsubstantially transversely to said coherent light beam and beingdisposed in parallel spaced apart relationship in the direction of saidlight beam from a foremost position on said frame proximal to said lasersource to a rearmost position on said frame distal to said laser source.4. The camera calibration target according to claim 3, wherein therespective points of adjacent ones of said series are transverselyshifted with one another within said arrangement and with respect to thecoherent light beam so as to prevent shading of said reflecting memberswhich may adversely affect said illuminated portions in forming saidimage.
 5. A camera calibrating apparatus for use with a laser sourcecapable of generating a beam of coherent light defining a calibrationplane, said camera being characterized by intrinsic imaging parametersand a field of view in the direction of an optical axis forming apredetermined angle with said calibration plane, said beam intersectingthe field of view of said camera to define an object imaging area, saidapparatus comprising: a calibration target including: a frame defining acoplanar arrangement of reference points having known positioncoordinates within an object reference system associated with said frameand defining at least two dimensions, said frame being capable of beingdisposed in a camera calibration position wherein said coplanararrangement of reference points is substantially parallel to saidcalibration plane; and an arrangement of light reflecting membersprotruding from said arrangement of reference points in a directionsubstantially perpendicular thereto so as to extend within said objectimaging area when said frame is disposed in said camera calibrationposition to allow said camera to capture an image formed by illuminatedportions of said light reflecting members; and image processor means forestimating position coordinates of said illuminated portions within animage reference system associated with said camera, for associating theestimated position coordinates of each said illuminated portion withinsaid image reference system with the known position coordinates of acorresponding one of said reference points in relation with acorresponding one of said calibration planes within said objectreference system, for calibrating a camera model based on said intrinsicimaging parameters with said associated known position coordinates andestimated position coordinates, and for using said calibrated cameramodel to associate any position coordinates in said object referencesystem with corresponding position coordinates in said image referencesystem.
 6. The camera calibrating apparatus according to claim 5,wherein said reference points are located with one another within saidarrangement and with respect to the coherent light beam so as to preventshading of said reflecting members which may adversely affect saidilluminated portions in forming said image.
 7. The camera calibratingapparatus according to claim 5, wherein said coplanar arrangementincludes a plurality of reference points series extending substantiallytransversely to said coherent light beam and being disposed in parallelspaced apart relationship in the direction of said light beam from aforemost position on said frame proximal to said laser source to arearmost position on said frame distal to said laser source.
 8. Thecamera calibration apparatus according to claim 7, wherein therespective points of adjacent ones of said series are transverselyshifted with one another within said arrangement and with respect to thecoherent light beam so as to prevent shading of said reflecting memberswhich may adversely affect said illuminated portions in forming saidimage.
 9. A method of calibrating a camera characterized by intrinsicimaging parameters and a field of view in the direction of an opticalaxis, said method comprising the steps of: i) generating a beam ofcoherent light defining a calibration plane; ii) disposing said cameraso that its field of view in the direction of its optical axis forms apredetermined angle with said calibration plane and so that said beamintersects the field of view of said camera to define an object imagingarea; iii) providing a calibration target including: a) a frame defininga coplanar arrangement of reference points having known positioncoordinates within an object reference system associated with said frameand defining at least two dimensions; and b) an arrangement of lightreflecting members protruding from said arrangement of reference pointsin a direction substantially perpendicular thereto; iv) disposing saidframe in a camera calibration position wherein said coplanar arrangementof reference points is substantially parallel to said calibration planeso that said light reflecting members extend within said object imagingarea; v) generating with said camera an image formed by illuminatedportions of said light reflecting members; vi) estimating positioncoordinates of said illuminated portions within an image referencesystem associated with said camera; vii) associating the estimatedposition coordinates of each said illuminated portion within said imagereference system with the known position coordinates of a correspondingone of said reference points within said object reference system; viii)calibrating a camera model based on said intrinsic imaging parameterswith said associated known position coordinates and estimated positioncoordinates; and ix) using said calibrated camera model to associate anyposition coordinates in said object reference system with correspondingposition coordinates in said image reference system.
 14. The cameracalibrating method according to claim 13, wherein said reference pointsare located with one another within said arrangement and with respect tothe coherent light beam so as to prevent shading of said reflectingmembers which may adversely affect said illuminated portions in formingsaid image.
 15. The camera calibrating method according to claim 13,wherein said coplanar arrangement includes a plurality of referencepoints series extending substantially transversely to said coherentlight beam and being disposed in parallel spaced apart relationship inthe direction of said light beam from a foremost position on said frameproximal to said laser source to a rearmost position on said framedistal to said laser source.
 16. The camera calibration method accordingto claim 15, wherein the respective points of adjacent ones of saidseries are transversely shifted with one another within said arrangementand with respect to the coherent light beam so as to prevent shading ofsaid reflecting members which may adversely affect said illuminatedportions in forming said image.